Cost - Benefit Analysis of the German High Speed Rail Network

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Undergraduate Economic Review

Volume 12 Issue 1 Article 4

2015

Martin Dorciak Lewis & Clark College, [email protected]

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Recommended Citation Dorciak, Martin (2015) "Cost - Benefit Analysis of the German High Speed Rail Network," Undergraduate Economic Review: Vol. 12 : Iss. 1 , Article 4. Available at: https://digitalcommons.iwu.edu/uer/vol12/iss1/4

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Abstract This study undertakes a cost-benefit analysis of the German ailwar y market looking specifically at the effects of high-speed rail development on railway passenger subsidies. Using OLS regression analysis, I estimate a demand curve for the German railway network at the route level; this is combined with cost curve estimates to yield a required subsidy for rail development assuming a natural monopoly market structure. I find that an increase in demand as a result of the introduction of high-speed rail technology causes a 23.9% decrease in required rail subsidies.

Keywords Consumer Surplus, Cost Benefit, Cost ffE ective, Elasticity of Demand, Railways, Regional Transportation, Transportation

This article is available in Undergraduate Economic Review: https://digitalcommons.iwu.edu/uer/vol12/iss1/4 Dorciak: German High Speed Rail

1 Introduction

Medium distance travel oﬀers the widest array of choices for travellers

in terms of modes of transport. Within the past 30 years, the advent of

high-speed rail technology has once again enabled rail to be a player in

medium distance travel of 200 to 500 miles, enabling railways to compete

with the currently more appealing modes of cars and planes by reducing the

costs and travel time associated with rail travel. The current developments

in railway transport have allowed rail to increase its modal share relative to

the other two modes, where modal share is the percentage of passengers that

utilize one mode relative to all available options. The main motivation of

this study is to estimate the impact of high-speed rail (henceforth referred to

as HSR) technology on the demand for rail transport and compare this with

the costs of implementing HSR. Then I comment on the viability of HSR as

an alternative option to air and vehicular travel. I will look speciﬁcally at

the case of Germany and comment on the eﬀectiveness of the German HSR

experience in terms of costs and beneﬁts.

The roots of HSR analysis come from transport economics and valuations

of travel time and fare prices and how they aﬀect consumer demand. Given a

choice of modes on a given route, consumers choose the mode that minimizes

the total trip cost, which equals the sum of the fare, the cost of preliminary

transit (transit to a station/airport), wait times, and the cost of the actual

travel time itself. In the speciﬁc valuation of transportation demand, the

primary method is that of an aggregate transportation model, where ”the

demand for a given [mode in] the travel market is explained as a function of

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variables that describe the product or its consumers” (Small, 1992: 6). This

derivation of transport demand can be focused even further as in Domencich

and Krafts (1970) approach of direct demand modeling, where the dataset to

be analyzed is comprised of pairs of locations forming various routes in a city

or region from which travel statistics such as ridership ﬁgures, fare prices,

and regional statistics are regressed to determine an explicit demand curve

for the speciﬁed region. I will employ this particular method to estimate

demand, focusing on a route level analysis of the German railway network

while also diﬀerentiating between routes that have HSR service and routes

that do not.

On the supply side, looking at costs and market structures further reveal

key motivations for this study. The predominant market structure for

railroad systems is that of a natural monopoly, where large economies of scale

and prohibitively high startup costs limit the number of ﬁrms to one. Even

then however, the suppliers of rail service typically require subsidization to

prevent travel costs from being prohibitively high for the consumer. Mohring

(1972) provides a theoretical framework for optimal subsidization levels in

public transport and posits that if the average riders opportunity cost of

travel time is below the marginal cost of operating a transport system,

then to make marginal cost pricing viable transport providers would have to

subsidize fares to a level that equals the opportunity cost of the passengers

time. This can also be intuited in the case of the monopolistic railway

networks. But rather than subsidizing a consumers time, production costs

must be subsidized to make monopoly pricing viable.

This issue is certainly relevant to current political debates, with developments

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proposed in California and Texas funded by an 8 billion dollar allotment

from the 2009 American Recovery and Reinvestment Act (Peterman, 2009).

Currently, several Central and Western European countries have developed

HSR networks with varying degrees of coverage that oﬀer travellers overall

travel times which are shorter than ﬂying or driving at comparable or

lower prices for medium distances of 100 to 500 miles with almost exclusive

provision of services through state owned monopolies who in turn subsidize

construction costs and fares with government money. This is indicative

of the motivations behind my analysis, as it is in the interest of national

governments to pursue HSR development policies; I aim to comment on the

viability of these developments.

The core of my analysis will focus on the derivation of the demand

and cost curves through a regression analysis of German rail statistics,

speciﬁcally focusing on observations of city pairs where the quantity of

rail transport demanded is represented by the route ridership and price

is represented by the total cost to passengers on the given route. Additional

variables include a dummy variable indicating the presence of HSR on a given

route to diﬀerentiate between base level rail demand and high speed rail

demand, average population density of the departure and arrival destinations,

average GDP per capita of departure and arrival destinations, and travel

times and fare prices of the primary competitor in that of air travel. The

analysis combines this market demand curve (equal to marginal beneﬁt) with

costs incurred by the monopolist ﬁrm to determine the socially optimal level

of HSR utilization for the German market and comment on discrepancies

between optimal and actual levels of ridership and commensurate subsidy

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levels.

The paper will proceed as follows. Section 2 reviews the literature in the

ﬁeld looking at general theories of transportation economics as they pertain

to institutionally provided transport and subsidization of said transport,

and speciﬁc applications of HSR analyses estimating costs, demand, and

societal beneﬁts. Section 3 presents the economic framework typical to the

state monopolist market present in Germany and equates curves in the ideal

model with their function in my analysis. Section 4 presents the data and

regression analysis to derive the demand curve and the speciﬁcation of cost

curves and section 5 represents these graphically and determines the optimal

level of utilization and compares this with observed levels.

2 Literature Review

Mohring (1972) develops a model that illustrates the role of subsidization

in public transport systems and then applies his model to travel statistics

for city busses in the Minneapolis St. Paul area. Mohring provides a general

base for analysis of transport subsidization, and additionally provides speciﬁcation

of several key cost variables. First, Mohring notes how transport pricing

deviates from traditional price theory models, where travellers also provide

an input into the ﬁnal cost calculations in that of their travel time. This

makes the total cost to consumers of utilizing transport the fare that is

charged in addition to the opportunity cost of the journey for the consumer.

The model presented by Mohring is presented below on the folowing page

in Figure 1.

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Figure 1: Bus Transport Subsidies

The commodity detailed in the graph is bus rides; as such, cost is

represented as dollars per bus ride and quantity as bus rides per week, with

curves representing short run and long run marginal costs, long run average

costs, and average variable costs. Mohring assumes this form without alteration

[describes] bus operations that are subject to increasing returns and can be

applied practically to metropolitan transit systems (Mohring, 592, 1972).

Additionally, a demand curve is implied as intersecting marginal costs at

point C. This model reconciles both the inputs of the consumer in that

of travel time and the producer in that of the bus system and widgets

are transformed into journeys. Mohring assumes a consumer provides time

inputs valued at E for point B on the average variable cost curve, noting the

curves representation of consumer valuation of time. Then, Mohring notes

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fare price at the level F, where demand intersects marginal costs. This would

generate what Mohring refers to as quasi-rent for bus services of EBCF, but

ultimately this falls short of the costs of ﬁxed inputs, and requires a subsidy

of FCDG to meet those input prices. I will use a variant of this model,

representing a natural monopoly structure to estimate required subsidies to

supplement fare revenues, something I will elaborate on in section 3.

Empirical studies of HSR focus predominantly on route level and network

(national) level analyses. Couto and Graham (2007) conduct one such

analysis, speciﬁcally looking at the impact of HSR service on quality and

speed of travel and the commensurate aﬀect on their derivation of a rail

demand function at national levels. The study ﬁrst posits a basic demand

relationship where a demand for railroad services is expressed as a function

of fare price, level of income, and other factors such as the presence of

HSR (represented as a dummy), geographical and economic conditions such

as regional incomes and city size of destinations, and prices of alternate

modes of travel (Cuoto and Graham, 114, 2007). To estimate their model,

Cuoto and Graham use a log-linear form 2SLS model to estimate coeﬃcients

that are themselves the respective [demand function] elasticities (Cuoto and

Graham, 120, 2007). They regress y passenger-kilometers per kilometer of

network length, (roughly an indicator of network utilization relative to the

size of the network) on four dummy variables representing the introduction

and use of two diﬀerent HSR technologies (conventional HSR, and tilting

HSR which runs on existing lines).

Additional variables include fare prices, alternate transport prices, and

national geographical and economic indicators. Cuoto and Graham chose

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the 2SLS model due to the structure of their variable representing railway

demand. The demand variable took the form of passenger kilometers per

kilometer of network length, and the 2SLS form was necessary due to the

endogeneity of passenger kilometers (a measure of total kilometers travelled

by all passengers) in their regression. Their regression results indicate

a price elasticity of demand of -0.22, which is in line with estimates of

price elasticity from similar studies by Fitzroy and Smith (1995,1998) and

McGeehan (1984). They further ﬁnd that conventional high-speed technology

increases railway demand overall at a national level, which coincides with

Fowkes and Nash (1991) who concluded that regardless of speed increases,

demand for rail travel will raise with the presence of a national HSR network.

In turn this suggests a 9% increase in passenger demand for railway travel

given the existence of a HSR network. The variable for tilting high-speed

technology was not found to be statistically signiﬁcant.

Ultimately Cuoto and Graham conclude that if railway development is

to be supported, then HSR technology is a viable method to increase rail

demand. The study concludes with a brief statement as to the beneﬁts

of HSR investment in that both tilting and conventional HSR can result

in increased demand with tilting technology requiring a much lower initial

investment (due to utilization of exiting networks) but only increasing demand

due to increased frequency, and conventional technology requiring a much

higher investment but resulting in greater overall demand. This is key to my

study and is a central assumption that I will test for the German market.

Rather, that HSR service inherently increases demand on a given route, as

opposed to a network. The magnitude increase estimated by Cuoto and

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Graham will also be useful to compare my conclusions to and to note the

diﬀerence in magnitudes between route level and network level analyses.

Behrens and Pels (2010) look speciﬁcally at intermodal competition

on the London Paris corridor where they work to determine passenger

choices between HSR and air travel from passenger preferences as observed

surveys and explicit ridership data. Behrens and Pels utilize nested logit and

mixed logit models to explain passenger choice on the London Paris route.

Their study draws from past work utilizing logit regressions to determine

passenger behavior, and draw their key variables from these studies in that

of fares, accessibility (to transport), frequency (of oﬀered journeys on a

route), and reason for travel (leisure or business). Speciﬁcally, Behrens and

Pels use similar characteristics in that of travel costs and times for rail

and substitutes, frequency, delay times, and personal statistics; they also

diﬀerentiate regressions between leisure travellers and business travellers

under the assumption of diﬀerent values placed on particular characteristics.

The model speciﬁed takes two forms, ﬁrst a nested form where choice of

mode is nested ﬁrst by type (air or rail) and then by speciﬁc route (arrival

and departure airport pairs and diﬀerent HSR services). The second form

merely groups all the possible routes into one group and assumes consumers

choose mode and route in one step. Their results concluded that HSR is a

viable competitor for air travel on the speciﬁed route. Business travelers in

particular were found to choose HSR due to their frequency of service over air

travel. Conversely, it was found that leisure passengers tended to substitute

into HSR in the face of rising airfare costs, and the relative stability of HSR

fares. The authors additionally note that several of the ﬂights (by various

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airlines) between the cities that they used in the model have since been

discontinued, showing the practical eﬀects of passengers choosing HSR over

air travel on routes where airlines encounter strong competition from rail.

Both this study and Cuoto and Graham provide insight into my own study

regarding how to approach the functional form of my demand regression as

well as detailing key variables of interest.

On the supply side, Levinson, Mathieu, Gillen, and Kanafani (1997)

conduct a theoretical study to estimate the full costs of developing a high

speed rail corridor in the state of California based on past observations and

economic theory. Their primary motivation lies in determining the private

and social costs of providing an intercity HSR network and to determine

what these costs imply when looking at HSR investment as opposed to

air travel and highway infrastructure investment. One of the key issues

with such an analysis as noted by the authors is the diﬀerentiation between

costs paid by the users of the transport mode and costs paid by others.

Their taxonomy for full cost to society (FC) includes numerous variables

but chieﬂy among them are infrastructure costs for construction (IC) and

maintenance (MC) of the rail network, carrier capital and operating costs

incurred by operators of rail service for the purchase of vehicles and other

items (CC), user money costs (fares and fees, FF), user travel time costs

(opportunity cost of passengers, represented by TC), user delay costs (opportunity

cost of delays, DC), and social costs incurred by people exogenous to the

system in that of emissions and noise pollution (SC). The full cost of high-speed

rail development and operation on a given route is thus calculated as a sum

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of the aforementioned values and takes the following form.

FC = IC + MC + CC + FF + TC + DC + SC (1)

The authors follow this speciﬁcation with the caveat that ”each cost is

a function of various parameters and depends on the level of [ridership]”

and devote the remainder of the paper to estimate these costs as functions

of ridership (Levinson et al, 192, 1997). The infrastructure costs are stated

as the costs of building the rail network and all that entails in terms of

structures, rail, power, and earthworks; this is simply divided by the number

of passengers utilizing the system to determine costs per passenger and leads

to a negatively sloped average infrastructure cost as ridership increases.

Carrier costs follow and are divided into two parts, namely carrier operating

and capital costs. Both are determined by multiplying the cost per unit by

the number of units in operation (where unit refers to a train) for operating

expenses such as electricity and worker salaries, and capital expenses in

that of the cost of the train. These costs will only vary with the number

of units in service and assuming the rolling stock of rail companies remains

constant in the short run, the marginal costs of accommodating additional

travellers on a given train is essentially ﬁxed. This study is unique among

others in that the authors account fully for all costs incurred whereas other

studies focus only on some sources of costs and quantify them diﬀerently

(such as cost per passenger-kilometer, or passenger journey), Levinson et.

al. instead focus on the full costs incurred by society. The remaining costs

are noted as incurred by the consumer and the public in general. The

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authors posit theories for the remaining factors where noise and pollution

can be interpreted by variations in housing price around HSR lines, but this

section is generally speculative.

Levinson et. al. use these costs to determine the total cost per user

of the system and compare it to the costs of air and vehicular travel.

Additionally the authors continue to tie their estimates back to the proposed

Californian HSR network. Their analysis and cost calculations are based on

data from the European Union and Japan, however the authors acknowledge

the diﬀerences and diﬃculty in comparisons of developments in other countries

and the United States. The authors conclude by noting that it would be

diﬃcult to implement HSR in California without massive subsidization and

even then so with higher subsidization than other countries. This is due

to constraints on federal spending, the deregulated nature of air transport

providing cheaper airfares (which was largely state directed in Europe and

Japan during the advent of HSR), and the sheer geographical distances

between Californian cities. However, the cost curve speciﬁcations in this

model can be incorporated into the theory of Mohrings model and applied

to the German case.

3 Economic Theory

The essential theory of my analysis requires several preliminary model

speciﬁcations and assumptions. First, it is important to note the prevailing

market structure in HSR before pursuing further speciﬁcity. As is the case of

most public transport goods, HSR networks are integrated into state owned

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railway companies and take the form of a natural monopoly (Mohring, 1972).

Speciﬁcally, the railway industry has very high costs of production with the

good in question being transport, but small and constant marginal costs;

also featured are large economies of scale and a large infrastructure that is

consolidated under the monopolist ﬁrm.

3.1 German Railway Market Structure

In the case of Germany, national transport and freight railroad is consolidated

under Deutsche Bahn AG (henceforth referred to as DB), a private joint-stock

company with 100% ownership by the German government (Deutsche Bahn).

Dunn and Perl (1994) provide further information on the formation and

structure of this network; DB stretches back to the Cold War and the

reuniﬁcation and integration of the two Germanies and how this eﬀected

the formation of a national railway system. This national disunity could

explain the slow pace of the introduction of Germanys high-speed Intercity

Express (ICE) train network. Additionally, the paper provides other details

that are not mentioned in economic analyses that shed light on some added

costs and rationale as to why the German network took the form that it

did. The primary diﬀerence between German and other HSR according to

the authors is the German utilization of standard previously existing track

for both passenger and freight transport upgraded to handle HSR trains, a

choice made to avoid prohibitively expensive costs of tunneling new HSR

lines through mountains. This has several economic implications, namely

the cost savings as opposed to constructing a new network, and the slightly

slower travel times on German HSR relative to France and other nations.

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All of this can be combined into a general model for a given railway

route in Germany that I will use in my study, presented below in Figure 2.

This model takes an adaptation of the general form presented by Mohring

Figure 2: Railway Route Model

(1972), where D = MC is the fair market fare price including time valuation,

and MR = MC is the fare price charged. MC in this case is ﬁxed due to

the ﬁxed nature of accommodating an additional passenger on rolling stock

that has already been purchased, this is to say, assuming a ﬁxed number

of trains running a ﬁxed number of routes, the cost of accommodating an

additional passenger on a train is constant. Marginal revenue is derived

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from the demand curve by transforming demand into total revenue and then

taking the derivative, from which I can determine the fare price charged on a

given route by looking at the intersection of marginal revenue and marginal

costs. As in a traditional monopoly, this determines the price and from

that I can determine realized producer surplus as indicated above in Figure

2. This however falls short of the AFC curve, which here represents the

infrastructure costs per rider incurred by DB in the construction of rail

lines and modiﬁcation of existing lines to accommodate high-speed trains.

It is here that Mohrings theory comes in to play with DB being unable to

cover total costs at any price or ridership level thus requiring subsidization to

cover all costs. As follows, the distance between D and AC at the monopolist

price level (the distance between Fare and Total Cost in Figure 2) is equal

to the subsidy needed to cover all costs that are not incurred by riders at

the monopolist price level. Additionally important to mention, due to the

nature of my data this model compares costs and demand at the route level,

where a route is deﬁned as a path of travel between a city pair, rather than

looking at the railway network in Germany as a whole.

This ultimately leads to the key point of interest in my study. A central

assumption to my model is borrowed from Mohring in that of an average

cost curve that is higher than demand for all quantities of passengers, and

thus unlike a standard monopolist ﬁrm, railroad providers cannot charge a

fare that will recoup all infrastructure and rolling stock costs and be low

enough to maintain any passenger levels. In regards to HSR, Cuoto and

Graham (2007) concluded that the presence of HSR led to an across the

board increase in demand for rail service, in line with other studies. In the

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model this translates to a shift outward in the demand curve for a network

with HSR service and as such leads to a higher ridership level and a lower

required subsidy. This change in required subsidy level will be the key focus

of my analysis, looking at if the introduction of HSR provides any meaningful

magnitude change in the level. The next two subsections will focus on the

speciﬁcation of the functional form of the demand and cost curves used in

my model.

3.2 Railway Demand

The central component of this study focuses on estimating a demand

curve at the route level of the German railway network. I will estimate a

linear demand speciﬁcation for a given German route that takes the form

of a traditional linear demand curve. The components that determine the

curve are total cost (TC) of a rail journey to a consumer and quantity of rail

travel demanded (D), which is represented by the number of rail passengers

on a given route as used by De Rus and Inglada (1997) to estimate railway

demand in Spain. As such, the relationship of interest is how the number

of rail passengers responds to changes in the total cost of a given journey.

The speciﬁc functional form of the regression utilized is as follows.

D = β0 + β1TC + β2X2 + ... + βnXn + (2)

This again represents the form assumed above, where railway demand is

dependent on total cost of travel, with other explanatory variables also

included. This regression yields an inverse function explaining the change

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in quantity demanded as a function of price. The demand function can be

transformed,

β 1 TC = 0 + D (3) β1 β1

. This transformation allows my demand function to be represented graphically

alongside the remaining curves in my model by standardizing axis variables

and by retaining the relationships of interest yielded in the regression results.

3.3 Railway Costs

Costs in this model are relatively straightforward, and again are represented

as the costs to consumers at the route level. The unique aspect of Germany

and its usefulness in regards to this study is that of the nature of its

railway system. The beneﬁt lies in the fact that Germany uses the same

track network for both normal and HSR applications, with both freight

and passenger traﬃc also travelling on the same track. This is also a key

determinant of which railway lines in Germany received HSR upgrades;

while major population centers will be linked with high-speed service, the

uniﬁcation of freight and passenger traﬃc gives incentive to bring higher

speed service to industrial centers that may not have much consumer demand

for the service (Albalate and Germa, 2012). This would seem to further

support the choice of Germany as an ideal location for this study, where

passenger travel would seem to take a secondary role when it came to

developing HSR lines to that of freight transport, thus leading to the conclusion

that there may be some randomness in the distribution of the HSR treatment

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in my model (notwithstanding highly likely endogeneity issues between freight

and passenger transport between cities).

Ultimately, this suggests however that a route level analysis and comparison

of costs is viable as much of the German railroad network thus has a uniform

average cost per kilometer of track. First, it is necessary to specify the

average costs per passenger incurred by DB on infrastructure costs on a

given route. I am assuming variable costs to be negligible in my model,

as the two major cost groups (infrastructure and rolling stock) are both

ﬁxed for a given route, thus average costs would simply be ﬁxed costs of

infrastructure per route divided by passenger level. This simpliﬁcation

allows me to assemble a variable for route cost (RC) as the product of

average cost per kilometer and route length. This cost per route must then

be divided by the amortization period (AP) of the route development costs.

This is then divided by passenger level (n) to determine the average ﬁxed

cost per passenger at a given passenger level. This is represented as follows.

RC AC = AP (4) n

Additionally, since passenger level (n) is variable, this equation will take a

downward convex form. This is intuitively sound and can even be equated

to a long run average total cost exhibiting increasing returns to scale, given

my assumption of negligible short run variable costs.

Marginal costs in my model are held ﬁxed. This is rationalized due to the

ﬁxed capacity of the German rail system in that once trains are acquired, the

cost of accommodating an additional passenger on a train is ﬁxed up until

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the capacity of the system is reached and more trains must be purchased.

Currently, the German rail system is comprised of refurbished trains from

the 90s, newer low cost regional trains, and 67 high speed trains built by

Siemens AG. Even in this regard, Germany is ideal for this study as rather

than purchasing trains on an as-needed basis, DB purchased the trains in

two major transactions, one in 2000 acquiring 50 Siemens Velaro ICE 3 Class

trains with 30 years of maintenance and a second in 2008 with 17 Siemens

Velaro D Class trains for international use based in Germany (Siemens,

2008). Thus to determine the marginal cost per passenger I take the total

cost (TC) of all rolling stock acquired by Deutsche Bahn and divide it by

the number of years in the period of amortization (AP) of the funds used

to purchase the trains. This is then be divided by the annual maximum

theoretical ridership (total train capacity multiplied by number of trains

multiplied by journeys per day) (TR).

TC MC = AP (5) TR

The value represented here again is the marginal cost of accommodating

an additional passenger on a train to recoup the costs of the train and its

maintenance.

4 Empirical Application

My ﬁrst application is to estimate the demand curve for German rail

travel as detailed above in my theoretical discussion.

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4.1 Demand Curve Regression

The majority of the data being used in my analysis was acquired from

Eurostat, a Directorate General of the European Union tasked with gathering

and providing data on many societal aspects to institutions of the EU and

other parties. Data collected by Eurostat was most recently updated in a

complete state in 2010. The database contains travel statistics for all cities

in the countries of interest and allows the user to pair a departure city with

an arrival city and shows the total traﬃc between the two cities on a given

mode of transport in the survey year. From this, I assembled 100 pairs

of arrival and departure cities, half with high-speed rail service and half

without. These pairs were determined by looking at a map of the German

rail network and assembling the pairs, additionally a route was only given a

designation of ”High Speed” if the route had the high-speed service in 2010

(Raileurope). I then retrieved passenger data for my city pairs on both rail

and air travel; I also retrieved density and GDP per capita data for each

city, all from Eurostat. Fare price data was also collected for each route

for rail transport and air transport. The explicit variables to be used in

my regression and their meanings are presented in Table 1 along with their

sources. Totrailcost and totaircost consist of two components, ﬁrst is the

base fare charged to passengers for their journey, then added to this is the

opportunity cost which is simply calculated as the time a traveller could be

spent working, found by taking the average GDP per capita of the city pair

and dividing that by an average annual workload (8 hours a day, 5 days a

week). This is then divided by 60 to get the opportunity cost per minute,

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Table 1: Regression Variables

Variable Deﬁnition railpass (Eurostat: Railway Transport) Total railway passengers between the given city pair totrailcost (Deutsche Bahn) The fare cost and opportunity cost of a rail journey in dollars totaircost (Google) The fare cost and opportunity cost of an air journey in dollars density (Eurostat: Density) The average population density of the given city pair in people/SqKM gdpcap (Eurostat: GDP per capita) The average GDP per capita of the given city pair in Dollars hsr A dummy variable indicating the presence of HSR service on a given route

and multiplied by the number of minutes in the journey for both air and rail

transport.1 Determining railpass merely involved assembling the city pairs

in Eurostat and inputting the values into my own dataset. Density and

gdpcap were also straightforward and represent the average of the respective

metric in the destination and arrival city. Lastly, hsr was determined by

seeing which city pairs were positioned on a stretch of high speed line and

assigning a dummy value of 1 for high speed service and 0 otherwise2.

Summary statistics for the variables of interest are presented in Table

2. The ﬁrst apparent observation that can be made is in regards to costs,

1For rail travel time, the total time in transit was merely considered. For air travel time, I added two hours to the total ﬂight time to account for checking in and traveling to airports typically on the outskirts of cities. 2In the rare case that a route contained sections both on high speed and normal speed track, the dummy was assigned to the simple majority.

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Table 2: Summary statistics

Variable Mean Std. Dev. N

railpass 417255 681150 100

totrailcost 281.03 83 100

totaircost 392.47 134 100

density 2442 630 100

gdpcap 35963 5157 100

hsr 0.49 0.502 100

with air costs at a higher average level than rail costs. Air costs also vary

to a greater extent than rail costs with a higher standard deviation at $134

versus $83 for rail. This can be accounted for by looking at some of the

lower traveled city pairs, which can still sustain a rail link due to the low

marginal costs of rail operation given existing track between the two cities.

Realistically, Deutsche Bahn can raise prices on such routes to still keep

them aﬀordable, but to oﬀset potential lower demand; air companies cannot

do the same and must charge a higher price to recoup costs of ﬂying a low

demand route, should the plane not be full. Density and GDP per capita

statistics also fall in line with expectations, with GDP per capita being fairly

homogenous and density being decidedly less so3.

I will utilize an OLS multiple linear regression as speciﬁed in equation (2)

of my theoretical framework. Including the above variables, the regression

3This is as a result of looking at the standard deviations and means with standard deviation being 14.3% of the mean for gdpcap and 25.8% of the mean for density.

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will take the following form.

railpass = β0 +β1totrailcost+β2totaircost+β3density+β4gdpcap+β5hsr+

(6)

The initial regression indicated a heteroskedastic relationship after applying

the Breusch-Pagan Test, thus the following regression summary presented

in Table 3 was corrected for heteroskedasticity and is presented with the

robust standard errors.

Table 3: Estimation results : Route Demand

Variable Coeﬃcient (Std. Err.) Prob. T

totrailcost -3830 (585) 0.000

totaircost 2038 (372) 0.000

density 361 (82) 0.000

gdpcap 12 (10) 0.232

hsr 221484 (103346) 0.035

Intercept -748015 (445370) 0.096

N 100

R2 0.53

F (5,94) 21.212

The regression results indicate a relationship in line with the expectations

of my model, in that a dollar increase in fare price on a railway route

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will lead to a statistically signiﬁcant 3830-passenger decrease in annual

ridership. Also of inerest is the coeﬃcient on hsr, which again is in line

with the expectation in that the presence of HSR is estimated to increase

annual ridership by 221,484 passengers signiﬁcant at 98.2% conﬁdence. The

variables representing total air cost and density can also be rationally explained.

First, the coeﬃcient on totaircost is positive and indicates an increase in

total air cost of 1 dollar causes substitution of 2038 passengers per year into

the competition in that of rail travel, and is signiﬁcant at 97.2% conﬁdence.

Additionally, density also shows a positive coeﬃcient of 361 additional annual

rail passengers for an additional person/km2 of average density at more

than 99% conﬁdence. This can again be rationalized by the notion that

the larger average density of the route would imply a greater need for

travel among residents. Lastly, the coeﬃcient on gdpcap is not found to

be statistically signiﬁcant. An observation of a scatter plot showing the

relationship between gdpcap and railpass indicates a relatively uniform level

of rail ridership at all levels of GDP per capita which is intuitively sound

when the historical precedent of heavy railway use among Germans is taken

into account, particularly among the middle class. This is to say that

railway transport is and has been marketed as a mode of transport for

all socioeconomic bacgrounds with class based fares, more akin to air travel

than public transport. Regardless, the variable will still be included to avoid

potential omitted variable bias.

Shortcomings of this portion of the analysis are most evident when

looking at the goodness of ﬁt of the linear model estimated. The most

straightforward way to check for this is through an application of the Ramsey

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RESET test. The test yields an F-value of 20.37, which when compared

to an F-statistic of 2.71 at 3 and 91 degrees of freedom indicates that

a non-linear relationship has some explanatory power in determining the

dependent variable. This is further consistent with a scatter plot of the

two main variables of interest, totrailcost and totrailpass as seen below

in Figure 3. A simple observation of the scatter plot shows that there

Figure 3: Totrailcost and Totrailpass Scatter Plot

is indeed a negative relationship between rail costs and passengers, which

seemingly supports the linear estimation given by the regression. However,

the rapidly increasing passenger levels correlated with decreasing costs could

indicate an exponential or logarithmic relationship between the primary

variables of interest. I will however continue with my linear estimation of

the demand function with the justiﬁcation of it being simpler to integrate

a linear demand function into my model. Additionally, the RESET test

does not preclude a linear relationship but merely indicates that other

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speciﬁcations may be superior, and as such I will continue with the linear

model.

Lastly, misspeciﬁcations in the model and regression could be caused

by problems of multicollinearity, which should not arise due to the nature

of my data, but will be looked at anyway. Firstly, the variables do not

exhibit strong correlation to each other, and most are again statistically

signiﬁcant. I also calculated the variable inﬂation factor for the variables,

and this yielded values ranging from 1.02 to 1.24 for the variables in the

model. These values are interpreted by taking the square root, which then

gives the factor by which the standard error of a variable is inﬂated compared

to what it would be if there was no correlation between that variable and

others. In the case of my data, these values range from 1.01 to 1.11, and

are far below the accepted threshold for high multicollinearity of VIF = 5.

This combines to allow me to reasonably conclude that multicollinearity of

my variables is not an issue in my regression.

4.1.1 Demand Curve Estimation

I now specify the explicit demand curve according to the method laid

out in Section 3.2 and equation (3).4 Again, the regression I ran above

estimates the eﬀect of total costs on ridership levels, and would place cost

as independent and ridership as dependent if merely placed into a demand

function, essentially showing the inverse demand function. I could opt for

4Again, with the values from the regression being transformed according to β 1 TC = 0 + D (7) β1 β1

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regressing all the variables on price instead to bypass this step but the

coeﬃcients would be diﬀerent and not represent the relationship that I am

ultimately after. Additionally, my model utilizes the other control variables

to determine a more precise estimate for the coeﬃcient on railpass and the

alternate model would not indicate this eﬀect in my desired relationship.

To continue, according to equation (2) my demand function for German

railway routes is,

1 TC = 195 − n (8) 3830

with TC representing the total cost of rail usage, and n representing the

passenger level. This simply indicates that starting at a peak price of $195

(vertical intercept), a one-dollar decrease in price will increase ridership

by 3830, to a horizontal intercept of 746,850 passengers. The inclusion of

the eﬀects of HSR into this will shift this demand curve upward to a new

vertical intercept of 253, while still retaining the same slope and pushing the

horizontal intercept out to 968,990. This comes to indicate that the presence

of HSR on a given route will increase demand for rail travel on that route

by approximately 23%.

This is greater than the estimated increase in demand of 9% referenced

by Cuoto and Graham earlier, but we must remember that this level was

estimated for the impact of HSR on national railway demand rather than

route level demand. This however is not out of line with intuition, as a

national presence of HSR might be small relative to the size of a network.

Thus only a small portion of the population that lives along the routes that

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HSR services and has access to it and their increased demand would be

counteracted by the relatively stable demand on other routes with no HSR

service. Conversely, my higher estimate for route level demand increase

reﬂects the (reasonably) larger increase in demand of people who have direct

access to the good. This demand function will be revisited later when the

full model is assembled, and the following section will focus on determining

the cost curves in my model.

From this demand curve, I can also simply determine the marginal

revenue curve necessary for the model through basic economic relationships.

Given that total revenue = price x quantity,5 I can take my demand function

and multiply by quantity as follows to determine total revenue, multiply

quantity through the equation, and take the derivative to yield marginal

revenue as follows.

1 1 TR = TC = (195 − n)n or T R = 195n − n2 (9) 3830 3830

δT R 1 MR = = 195 − n (10) δn 1915

This marginal revenue curve maintains the same intercept as the total cost

but with half of the slope and represents the marginal revenue of each

additional passenger on a given route. It will be revisited and incorporated

into the overall model to determine the monopolist price level, and the

required subsidy level.

5With my variables of TC and n equaling price and quantity respectively.

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4.2 Cost Curve Estimation

The estimation of cost curves for the model is generally fairly straightforward,

but still require some explanation. With demand estimated, I will ﬁrst focus

on average ﬁxed costs. In my case, AFC is being determined purely as the

infrastructure construction costs necessary to build a given routes track at

a given passenger level. This can also be equated to overall average costs,

as I noted in Section 3 with my assumption of negligible variable costs. To

reiterate, Germany is an ideal choice on these grounds for this analysis as

all German trains have the ability to run on all types of track, unique to the

German rail network and allowing me to utilize a simple average construction

cost per mile of track to apply to my entire analysis. First, to determine

a total variable for route cost I took the average cost per mile in dollars of

the network (23.1 million per mile) and multiplied this cost by the length

of each route in miles to yield a variable for total route cost (Feigenbaum,

2013). These total route costs are then divided by 10 years, which is the the

amortization period of loans used to fund the construction and the average

is taken, giving an average route cost per year of $54.18 million.

To determine the actual formula for AC I will follow the method speciﬁed

in section 3.3 and following equation (4). This simply takes the above value

of average cost per year and divides it by passenger level (n) to determine

the average costs at a given passenger level. The explicit form taken by the

AC curve is as follows.

54180000 AC = (11) n

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This gives a downward sloped and convex AFC curve, which as discussed

previously, can be equated to ATC, given my assumption of negligible variable

costs. The curve itself determines the necessary subsidy level, with the

monopolist passenger quantity being taken up to the AFC curve, which gives

the price level necessary to charge riders to recoup infrastructure costs.

Marginal costs are held constant in my model and are represented as the

cost of accommodating an additional passenger on any given route covering

the costs of rolling stock and maintenance. This ﬁxed level of marginal

cost per route passenger will be determined according to equation (5) that

again takes the total cost of all rolling stock and divides it by the number

of years over which the funds used to purchase the trains are amortized.

Then the cost per year is divided by the maximum theoretical ridership to

determine the marginal cost of accommodating an additional passenger. The

calculation is very straightforward, but values and intuition of results are

still necessary to discuss. Values for the cost of train units are determined

from Siemens AG, the provider of all rolling stock. Converted into dollars,

the approximate cost per train unit purchased by DB is $41,500,000 and

is paid for over 10 years with maintenance included in the purchase price

(Siemens, 2008) Additionally necessary to account for are energy and labor

costs per train which are estimated to be $1,168,000 per train in energy

and $800,000 per train in labor costs which are added to the cost per unit

(Feigenbaum, 2013). This is then multiplied by 67, or the number of recently

(since 1998) purchased train units in operation to yield a total cost of rolling

stock and maintenance of approximately $2,912,356,000 which when divided

by 10 years gives an annual cost of $291,235,600.

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The total annual cost must then be divided by maximum theoretical

annual ridership to determine the marginal cost of an additional passenger.

The maximum capacity of one DB train unit is on average 430 passengers,

and in between trains in maintenance time, and rotation of older train stock

on routes, I will assume each new train makes an average of one journey per

day. The average capacity per train of 430 is multiplied by 67 trains and 365

days for a total of 10,515,650 possible passengers in a given year. When the

annual cost is divided by the maximum possible ridership it is determined

that the marginal cost of an additional passenger is $27.70. Intuitively, this

indicates that for any additional passenger on any route, $27.70 of their fare

price will always be required to cover the train units and their operation.

The next section will focus on incorporating this marginal cost curve and

all previous curves into my model and determine the change in subsidy level

resultant from a shift in the demand curve brought about by the presence

of HSR.

5 Cost-Beneﬁt Analysis

5.1 Subsidy Calculation

Now, having derived all the necessary curves, I can assemble the following

graph for my model, representing a given German railway route without

HSR service, showing demand and costs. To note, the graph is not drawn

to scale due to the high passenger levels relative to costs. The main purpose

of this section is to look at the subsidy levels required to make a given

route ﬁnancially viable by oﬀsetting infrastructure costs and supplementing

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Figure 4: German Railway Route- No HSR

fare revenues. In Figure 4, this is represented as the shaded area marked

subsidy, comprising of the diﬀerence between fare revenues (FR) at the

monopolist price and the average cost curve. To begin the calculation, I will

ﬁrst determine the equilibrium level of passengers n*, on a given route by

setting marginal revenue equal to the marginal cost of 27.7 and solving for

n, which in this case yields a value of 320,380 passengers. This n* is then

inputted into the demand and AC equations to give the equilibrium fare and

infrastructure cost not covered by fare revenue which are $111.35 (Fare*)

and $169.11 (C*), respectively. Next, I will determine fare revenue by taking

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the diﬀerence of Fare* and marginal costs to give a revenue per passenger

of 83.65, this is then multiplied by the equilibrium ridership level n* to give

a fare revenue of approximately $26.8 million per annum on a given route

without HSR, represented in Figure 4 by the shaded region marked FR. The

required subsidy level is calculated similarly by taking the diﬀerence of C*

and Fare* and then multiplying by n* to get a reqiured annual subsidy of

$18.505 million per annum on a route.

The main statistic that this boils down to is that for a given non high

speed route in Germany, an annual subsidy of 34.2% of total costs is required

to supplement fare revenues and break even at the equilibrium price and

ridership level. In hindsight of looking at several other studies of current

required transit subsidies, my estimate would seem to understate the actual

level of subsidization present in much of Europe and America. For example,

rail projects in the UK and France typically subsidize total costs by two

thirds to arrive at the ﬁnal passenger fare (European Environment Agency,

2007). In America the levels are even higher, with an average of 70-80% of

costs being subsidized on commuter rail projects (Garrett, 2004). This can

lead to two conclusions, first that my figures and model are miss-specified,

which may account for some of the variation due to previously mentioned

simpliﬁcations I make, such as assuming demand to be linear and variable

costs to be negligible. Second, the nature of these cost-beneﬁt analyses

in general may result in an understatement of the required subsidy levels

(Utsunomiya and Hodota, 2011). This is to say that all cost-beneﬁt valuations

of existing systems undertaken to make future policy suggestions are chronically

unable to account for the full costs of rail development in terms of cost

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overruns, corruption, and ineﬃcient allocation of funds to truly come to a

reasonable policy conclusion based on ex-post data.

Still, the main goal of this study is to estimate the eﬀect of HSR on the

reqiured subsidy level according to my model. As noted previously in the

discussion of equation (10), the inclusion of the eﬀects of HSR service on

a given route increase demand by about 23% through the addition of the

hsr variable to the demand function. This increases the vertical intercept to

253 and retains the original slope for a new horizontal intercept of 968,990

passengers, the shift can be seen in ﬁgure 5.

Figure 5: German Railway Route- HSR

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This also shifts the marginal revenue curve as it is derived from demand

up to a vertical intercept of 253 and again at half the slope of demand, then

the same calcualtions as above are applied to determine fare revenue and

subsidy level.When equating marginal cost with the new marginal revenue

curve, a new passenger level of 431,450 is given. This is then put into

the new demand curve and the original cost curve to yield a fare and cost

per passenger of $112.65 and $125.58 respectively. Then fare revenue and

subsidy is calculated in the same manner as before to yield a fare revenue

of approximately $36,651,700 and a required subsidy of $5,578,650. This

indicates a required annual subsidy that is 10.3% of total annual costs. The

key statistic that I have reached in this section is the diﬀerence in required

subsidies between the HSR and non-HSR routes, which is found to be 23.9%,

thus indicating the presence of HSR (through its eﬀect on demand) causes

a 23.9% decrease in required rail subsidy. This is intuitively sound and in

line with my assumed model from Section 3, allowing me to conclude that

the rough model can indeed be applied to the German railway market as a

representation of its basic operation at the route level.

5.2 Model Shortcomings

There are some potential places for improvement and possibilities for

shortcomings in the model however. Most signiﬁcantly, the magnitudes

of shifts and changes in demand and subsidies are indeed fairly robust,

but are not very speciﬁc nor precise. The biggest shortcoming is most

likely in my estimation of average costs, which are understating their actual

levels as discussed above. There are indeed variable costs associated with

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rail travel, but I assumed them away for simplicity of the model, and

with the rationalization that they are relatively small compared to total

infrastructure costs, but nonetheless they are there and would increase

average cost per passenger. Additionally, my level of total route cost is

also understating actual total costs. Realistically, total cost would have to

be measured for each individual route and then regressed to determine a

more ﬁtting estimate for these costs for a given route. This is because I

took a mere average construction cost per mile and then averaging this for

each route, in reality the route construction costs vary wildly in regards

to environmental and urban obstructions that must be negotiated on some

routes, in rare cases being as much as double the average.

Another factor to consider is cost overruns and other expenses that are

not reported in some cases as part of the total construction costs, all of which

combine to indicate that my explicit example understates the total costs of

infrastructure, and in turn average costs per passenger. This indicates that

a more realistic account of costs would then lead to larger required subsidies

to make a route ﬁnancially viable, combined with my estimated demand. On

the note of demand, in preliminary observation, a logarithmic relationship

would be better suited to my dataset and yields a closer ﬁt, but I proceeded

with the linear regression to maintain model simplicity. Along these lines,

due to the convexity of the logarithmic function and an observation of the

scatter plot of the data points, I would conclude that I slightly overstated

the central range of passenger demand.

All of this combines to indicate what was mentioned previously, in that

most of these studies do not accurately represent the full costs and required

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subsidies necessary to support a rail system. However, it is still reassuring to

see that the directions of changes in the model all move as expected. As far

as policy implications, the true decisions lie with policy makers being able

to rationalize the cost to taxpayers against revenues brought in through

fares. The goal of policy makers in this regard is to ensure that demand

and fare revenues are maximized while costs and required subsidies are

minimized, to pass on a minimum of cost to taxpayers and lessen the double

payment made by riders, who essentially pay twice for their fares and in

taxes. This conclusion is not reached in my study, but with a more accurate

representation of costs, the general model could be used to determine this

level and comment on the eﬀectiveness of the implementation of the system

in Germany.

6 Conclusion

Much of the work done to analyze the costs and beneﬁts of HSR to

comment on policy choices presents an overly optimistic view and in many

cases fails to account for the full costs of a rail project. Given a natural

monopoly market structure with ﬁxed costs that exeed revenues for all levels

of demand, it is diﬃcult to comment on the viability of HSR investment

without context as to the ﬁnancial standing of a country and the ability of

policy makers to justify the cost to taxpayers. Looking at Germany, I worked

to apply a general model of railway subsidization to an ideal representation

of a high speed rail network with readily available data.

In my case, I found that Germany does conform to my model and

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additionally to previous studies such as that by Cuoto and Graham and

exhibits an increase in consumer demand on a given route with the presence

of HSR service. Required subsidies also decrease through a result of my

speciﬁed model, but there is much room for improvement upon my basic

framework. Most signiﬁcantly, an accurate account of all costs combined

with a better speciﬁcation of costs in the model would yield levels that are

more in line with real world observations of costs that require subsidies of

over 50%.

Assuming that my representation of a given German route is accurate, I

could reasonably reccommend for further high speed development as opposed

to basic railway development and maintenance due to a decrease in subsidies

and increase in fare revenues brought about through increased demand. But

again, before other developments proceed, such as that in California, I would

more conservatively suggest for analysts to look closely at full costs and

any potetnial for cost overruns to not understate cost levels, and also to

make sure an accurate representation of consumer demand is made to not

overstate demand. This will ultimately give policy makers a more accurate

representation of required subsidies and allow them to better justify these

costs to taxpayers.

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